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arXiv · 1608.06988

On nonsymmetric rank one singular perturbations of selfadjoint operators

Mykola Dudkin·Tetiana Vdovenko
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Abstract

We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form $\tilde A = A + \alpha\left\langle\cdot, \omega_1\right\rangle\omega_2$, $\omega_1\not = \omega_2$, $\alpha\in{\mathbb C}$, in a general case $\omega_1,\omega_2\in{\mathcal H}_{-2}$. Using a constructive description of the perturbed operator $\tilde A$, we investigate some spectral and approximations properties of $\tilde A$. The wave operators corresponding to the couple $A$, $\tilde A$ and a series of examples are also presented.

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Mykola Dudkin, Tetiana Vdovenko. 2016-08-24. On nonsymmetric rank one singular perturbations of selfadjoint operators. https://arxiv.org/abs/1608.06988

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